Image Filtering by Factorial Kriging—Sensitivity analysis and application to Gloria side-scan sonar images

Factorial Kriging (FK) is a data- dependent spatial filtering method that can be used to remove both independent and correlated noise on geological images as well as to enhance lineaments for subsequent geological interpretation. The spatial variability of signal, noise, and lineaments, characterized by a variogram model, have been used explicitly in calculating FK filter coefficients that are equivalent to the kriging weighting coefficients. This is in contrast to the conventional spatial filtering method by predefined, data-independent filters, such as Gaussian and Sobel filters. The geostatistically optimal FK filter coefficients, however, do not guarantee an optimal filtering effect, if filter geometry (size and shape) are not properly selected. The selection of filter geometry has been investigated by examining the sensitivity of the FK filter coefficients to changes in filter size as well as variogram characteristics, such as nugget effect, type, range of influence, and anisotropy. The efficiency of data-dependent FK filtering relative to data-independent spatial filters has been evaluated through simulated stochastic images by two examples. In the first example, both FK and data-independent filters are used to remove white noise in simulated images. FK filtering results in a less blurring effect than the data-independent fillers, even for a filter size as large as 9 × 9. In the second example, FK and data-independent filters are compared relative to the extraction of lineaments and components showing anisotropic variability. It was determined that square windows of the filter mask are effective only for removing Isotropie components or white noise. A nonsquare windows must be used if anisotropic components are to be filtered out. FK filtering for lineament enhancement is shown to be resistant to image noise, whereas data-independent filters are sensitive to the presence of noise. We also have applied the FK filtering to the GLORIA side-scan sonar image from the Gulf of Mexico, illustrating that FK is superior to the data-independent filters in removing noise and enhancing lineaments. The case study also demonstrate that variogram analysis and FK filtering can be used for large images if a spectral analysis and optimal filter design in the frequency domain is prohibitive because of a large memory requirement.